Expert models of multiobjective optimization

Abstract

An approach is proposed to solve a vector optimization problem for complex engineering and economic systems where the information about experimental and statistical data necessary to set up regression models is insufficient (or absent). To solve this problem, multiobjective optimization with nonlinear trade-off scheme is employed.There is often a lack of experimental and statistical data to develop necessary mathematical models for the optimization of complicated engineering and economic systems. The situation is worsened in case of the optimization with respect to several contradictory performance criteria.If there is an acute shortage of experimental data, we propose to obtain the necessary information ("quasiexperimental" data) from experts experienced in the design and maintenance of such complicated systems.The study is based on the example of multiobjective optimization of space engineering objects with respect to a generalized reliability-cost criterion; however, the results can easily be used in other subject areas. By the reliability we will mean the probability of the fact that the key parameters of all the elements of the object are within admissible limits.It is necessary to take into account that the case in hand is designing fundamentally new technological items for which performance indices considerably differ from those developers dealt with earlier or now. One of the particular aspects is the boundedness (or total absence) of experimental and statistical data that would be used to determine mathematical models of reliability and cost.These hardly formalizable conditions involve nonconventional approaches, one of which is considered in the paper. It is natural that in this case we can only mean preliminary calculations and approximate determination of the main tendencies when choosing the factors that influence the reliability and cost of space engineering objects being developed. PROBLEM STATEMENTTo solve the optimization problem, it is necessary to have the following data as the starting point for the mathematical model.

Elastic Damping Mechanism Optimization by Indefinite Lagrange Multipliers

“…The Lagrange multiplier method was applied to find a compromise solution based on the research results obtained from our early studies (equations (4), ( 5) and ( 6)). The process to obtain the compromise is described in detail in [39]. In this section of the current paper, we present an algorithm of actions for solving our compromise problem.…”

“…One of the main methods remains the transfer of constraints to objective function what was proposed by Lagrange. The Lagrange multiplier method is described in detail in [30], [39].…”